UW Combinatorics and Geometry Seminar: Michael Tang

The generalized degree polynomial (GDP) of a tree is an invariant introduced by Crew that enumerates subsets of vertices by size and number of internal and boundary edges. Aliste-Prieto et al. proved that the chromatic symmetric function of a tree, introduced by Stanley, linearly determines its GDP. We present several classes of information about a tree that are determined by its GDP (and thus its chromatic symmetric function). Examples include the double-degree sequence, which enumerates edges by the pair of degrees of their endpoints, and the leaf adjacency sequence, which enumerates vertices by degree and number of adjacent leaves. We also discuss a further generalization of the GDP which is also determined linearly by the chromatic symmetric function. (This is joint work with Ricky Liu.)